which takes into account both, the muon depolarization due to small disordered static internal fields of nuclear origin with a distribution width \(\Delta \) , as described by the standard Kubo-Toyabe function \(P_{\rm KT} (t,\Delta ,B)\)  [1]}, and the polarization decay due to fluctuating local fields of electronic origin, characterized by the stretched exponential function \(\exp [-(\lambda t)^\beta ]\) .
Here \(\lambda \)  is the corresponding muon spin relaxation rate and the stretching exponent \(\beta < 1\)  denotes a finite distribution of \(\lambda \) .
Weak nuclear magnetic fields and experimental background were determined from the field dependence of \(A(t)\)  at 275 K (see Supplementary Fig. 3), which gives \(\Delta =0.062\)  mT, \(\lambda = 0.005\)  \(\mu \) s\(^{-1}\) , \(\beta = 1\) , \(A_{0}=0.283\)  and \(A_{\rm bgd}=0.037\)  (in the dilution-refrigerator set-up the latter parameters are \(A_{0}=0.287\)  and \(A_{\rm bgd}=0.055\) ).
The muon relaxation at high temperatures and low applied fields is predominantly due to static nuclear fields, as the relaxation due to dynamical fields of electronic origin is weaker. Yet the letter remains the only relaxation mechanism once the applied field exceeds 1 mT (Supplementary Fig. 3).
With lowering temperature, however, the electronic dynamical relaxation mechanism becomes dominant even in zero applied field.
The temperature dependence of \(\lambda \)  is obtained from fits of equation (REF ) to the experimental \(P(t)\)  curves (Fig. REF a) and is shown in Fig. REF b, while the corresponding stretching exponent is shown in Fig. REF d.
We note that deviation of \(\beta \)  from unity at low temperatures can be understood within the scenario of strong exchange anisotropy governing the spin dynamics in the ground-state Kramers' doublet of NdTa\(_7\) O\(_{19}\) , resulting in a broad distribution of local fields at the muon site.
If, alternatively, \(\beta < 1\)  originated from muons stopping at multiple sites in the unit cell, this parameter would not change with temperature.
